Galois cohomology of abelian groups

Dalton Tarwater

Vol. 24 (1968), No. 1, 177–179

DOI: 10.2140/pjm.1968.24.177

Abstract

Normal and separable algebraic extensions of abelian groups have been defined in a manner similar to that of the field theory. In this paper it is shown that if N is a normal algebraic extension of the torsion group K = ∑ K_p, where the p-components K_p of K are cyclic or divisible, and if G is the group of K-automorphisms of N, then there is a family {G_E}_E∈X of subgroups of G such that {G,{G_E}_E∈X,N} is a field formation.

Mathematical Subject Classification

Primary: 20.30

Secondary: 18.00

Milestones

Received: 20 February 1967

Published: 1 January 1968